Brinson-Fachler

Decomposes a portfolio’s active return against a benchmark into allocation, selection and interaction effects, computed per asset and per date, then aggregated across time.

Formulas

For each asset on each date, with asset return \(r\), portfolio weight \(w_p\) and benchmark weight \(w_b\):

\[\begin{split}r_p &= w_p \cdot r &&\text{portfolio contribution} \\ r_b &= w_b \cdot r &&\text{benchmark contribution} \\ \alpha &= r_p - r_b &&\text{active return} \\ \text{allocation} &= (w_p - w_b) \cdot r_b \\ \text{selection} &= \alpha \cdot w_p \\ \text{interaction} &= \alpha - \text{allocation} - \text{selection}\end{split}\]

Per-date totals are the sums across assets, and by construction

\[\alpha = \text{allocation} + \text{selection} + \text{interaction}\]

which is also equal to \(\text{portfolio\_return} - \text{benchmark\_return}\).

Implementation

The PyArrow-based implementation lives in BrinstonFachlerArrowAttribution, implementing BrinstonFachlerArrowInterface. A pandas-based reference implementation is also available as BrinstonFachlerAttribution. See Brinson-Fachler for the full API reference.

Enable this methodology by setting brinson_fachler_method = yes in attribution_analysis_parameters.xlsx (see Configuration Reference).